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1 Purpose

G02QFF performs a multiple linear quantile regression, returning the parameter estimates and associated confidence limits based on an assumption of Normal, independent, identically distributed errors. G02QFF is a simplified version of G02QGF.

2 Specification

3 Description

Given a vector of n observed values,
y=yi:i=1,2,…,n, an n×p design matrix X, a column vector, x, of length p holding the ith row of X and a quantile τ∈0,1, G02QFF estimates the p-element vector β as the solution to

minimizeβ∈ℝp∑i=1nρτyi-xiTβ

(1)

where ρτ is the piecewise linear loss function ρτz=z⁢τ-Iz<0, and Iz<0 is an indicator function taking the value 1 if z<0 and 0 otherwise.

The routine did not converge whilst calculating the parameter estimates. The returned values are based on the estimate at the last iteration.

2

A singular matrix was encountered during the optimization. The model was not fitted for this value of τ.

8

The routine did not converge whilst calculating the confidence limits. The returned limits are based on the estimate at the last iteration.

16

Confidence limits for this value of τ could not be calculated. The returned upper and lower limits are set to a large positive and large negative value respectively.

It is possible for multiple warnings to be applicable to a single model. In these cases the value returned in INFO is the sum of the corresponding individual nonzero warning codes.

12: IFAIL – INTEGERInput/Output

On entry: IFAIL must be set to 0, -1​ or ​1. If you are unfamiliar with this parameter you should refer to Section 3.3 in the Essential Introduction for details.

For environments where it might be inappropriate to halt program execution when an error is detected, the value -1​ or ​1 is recommended. If the output of error messages is undesirable, then the value 1 is recommended. Otherwise, if you are not familiar with this parameter, the recommended value is 0. When the value -1​ or ​1 is used it is essential to test the value of IFAIL on exit.

On exit: IFAIL=0 unless the routine detects an error or a warning has been flagged (see Section 6).

6 Error Indicators and Warnings

If on entry IFAIL=0 or -1, explanatory error messages are output on the current error message unit (as defined by X04AAF).

8 Further Comments

9 Example

A quantile regression model is fitted to Engels 1857 study of household expenditure on food. The model regresses the dependent variable, household food expenditure, against household income. An intercept is included in the model by augmenting the dataset with a column of ones.